Symmetric Vacua in Heterotic M-Theory

TL;DR

This paper investigates symmetric vacua in heterotic M-theory on Calabi-Yau three-folds, showing their non-existence in elliptically fibered cases but providing explicit examples in other geometries, with implications for phenomenology.

Contribution

It demonstrates the non-existence of symmetric vacua in elliptically fibered Calabi-Yau spaces and constructs explicit examples in other Calabi-Yau geometries, analyzing their phenomenological properties.

Findings

Symmetric vacua do not exist for elliptically fibered Calabi-Yau spaces.

Explicit symmetric vacua are found in Calabi-Yau three-folds from intersections in projective spaces.

Low energy effective actions of these vacua have no perturbative threshold corrections.

Abstract

Symmetric vacua of heterotic M-theory, characterized by vanishing cohomology classes of individual sources in the three-form Bianchi identity, are analyzed on smooth Calabi-Yau three-folds. We show that such vacua do not exist for elliptically fibered Calabi-Yau spaces. However, explicit examples are found for Calabi-Yau three-folds arising as intersections in both unweighted and weighted projective space. We show that such symmetric vacua can be combined with attractive phenomenological features such as three generations of quarks and leptons. Properties of the low energy effective actions associated with symmetric vacua are discussed. In particular, the gauge kinetic functions receive no perturbative threshold corrections, there are no corrections to the matter field Kahler metric and the associated five-dimensional effective theory admits flat space as its vacuum.